The out-of-court mediation won’t address all disputes between the companies. Alere says Abbott is seeking to unfairly back out of the deal while Abbott says its acquisition target has withheld information about federal bribery probes.

“It is imperative that mediation occur immediately” to resolve questions about whether Abbott’s efforts to win regulatory clearance from US and foreign regulators violated the deal’s terms, Alere said in a letter filed Wednesday in Delaware Chancery Court.

Officials of Waltham-based Alere and Abbott Park, Ill.-based Abbott declined Wednesday to comment beyond the letters on the agreement to mediate the antitrust dispute they submitted to Judge Sam Glasscock.

The proposed purchase, signed Jan. 30, ran into trouble after Alere delayed filing documents about its 2015 financial performance with securities regulators. That prompted Abbott to accuse Alere of failing to meet disclosure requirements under the merger agreement. Alere has since disclosed two US probes into some of its businesses overseas and its billing practices in the United States.

Abbott also contends that Alere didn’t turn over information about the company’s foreign operations that are facing bribery probes. Federal prosecutors have issued grand-jury subpoenas for information about Alere’s operations in Asia, Africa, and Latin America.

Alere, on the other hand, contends Abbott officials got cold feet about the takeover after agreeing to buy medical-device maker St. Jude Medical Inc. for $25 billion in April.

Closing both deals would stretch Abbott’s financial limits, forcing the company to issue more equity and triple “its debt load, which will likely lower its credit rating,” Alere contends in court papers.